Null and Alternative Hypotheses In a hypothesis test, sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population.…
Tests on Means Example 9.8 Problem Jeffrey, as an eight-year old, established a mean time of 16.43 seconds for swimming the 25-yard freestyle, with a standard deviation of 0.8 seconds. His dad, Frank, thought that Jeffrey could swim the 25-yard freestyle faster using goggles.…
Earlier in the course, we discussed sampling distributions. Particular distributions are associated with various types of hypothesis testing. The following table summarizes various hypothesis tests and corresponding probability distributions that will be used to conduct the test (based on the…
When you perform a hypothesis test, there are four possible outcomes depending on the actual truth (or falseness) of the null hypothesis H0 and the decision to reject or not. The outcomes are summarized in the following table: Statistical Decision H0 is actually……
The actual test begins by considering two hypotheses. They are called the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints. H0: The null hypothesis: It is a statement of no difference between the variables–they are not related. This can often be considered the…
Figure 9.1 You can use a hypothesis test to decide if a dog breeder’s claim that every Dalmatian has 35 spots is statistically sound. (credit: modification of work “black and white, view, dog, animal, fur, mammal, garden, head, vertebrate, beautiful, elegant, rush,…
A Confidence Interval When the Population Standard Deviation Is Unknown and Small Sample Case In many cases, the researcher does not know the population standard deviation, σ, of the measure being studied. In these cases, it is common to use the…
Continuous Random VariablesUsually we have no control over the sample size of a data set. However, if we are able to set the sample size, as in cases where we are taking a survey, it is very helpful to know…
During an election year, we see articles in the newspaper that state confidence intervals in terms of proportions or percentages. For example, a poll for a particular candidate running for president might show that the candidate has 40% of the vote within…
In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence…